If the interval of $[t_0,T]$ divided to $n$ equal part, then we have $n$ integral of the form $(*)$ where $t_i$ is the lower bound of each interval. Also I'm willing to plot the result of $n$ integration.

In MATLAB it's easy to code the above integral; by defining a for loop, one can deal with sweeping t over interval $[t_0,T]$.

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